论文标题
多步完全离散的有限元方法的最大规律性用于抛物线方程
Maximal regularity of multistep fully discrete finite element methods for parabolic equations
论文作者
论文摘要
本文将半分化的最大$ l^p $ -Reculacultity在[27]中延伸到多步完全离散的有限元方法，用于抛物线方程，其中更通用的扩散系数在$ w^{1，d+β} $中，其中$ d $是空间的尺寸和$β> 0 $。 $ r $ bundedness的最大角度分别针对分析性半群$ e^{za_h} $和分辨率运算符$ z（z-a_h）^{ - 1} $，与椭圆形有限元操作员$ a_h $相关。最大$ l^p $ - 最佳$ \ ell^p（l^q）$错误估计和$ \ ell^p（w^{1，q}）$估计是用于具有多步向后分化公式的完全离散有限元方法的完全离散有限元方法。
This article extends the semidiscrete maximal $L^p$-regularity results in [27] to multistep fully discrete finite element methods for parabolic equations with more general diffusion coefficients in $W^{1,d+β}$, where $d$ is the dimension of space and $β>0$. The maximal angles of $R$-boundedness are characterized for the analytic semigroup $e^{zA_h}$ and the resolvent operator $z(z-A_h)^{-1}$, respectively, associated to an elliptic finite element operator $A_h$. Maximal $L^p$-regularity, optimal $\ell^p(L^q)$ error estimate, and $\ell^p(W^{1,q})$ estimate are established for fully discrete finite element methods with multistep backward differentiation formula.
